Methods and apparatus for self-inverting turbo code interleaving with high separation and dispersion

ABSTRACT

The present invention provides methods for generating self-inverting turbo code interleavers having high separation and high dispersion characteristics. Methods are provided for deterministically generating self-inverting turbo code interleavers from a specification for an existing non-self-inverting interleaver. Methods are also provided for randomly generating self-inverting turbo code interleavers. The present invention also provides methods and apparatus for encoding digital data and communicating the digital data using self-inverting turbo code interleavers/de-interleavers.

This application claims the benefit of U.S. provisional patentapplication No. 60/382,493 filed on May 21, 2002, which is incorporatedherein and made a part hereof by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to digital communications systems,processes, apparatus and related software utilizing error-correctingcodes. More particularly, the invention relates to self-invertinginterleavers/de-interleavers for use with wireless communication systemsthat rely on turbo codes to perform signal error-correction.Accordingly, the general objects of the invention are to provide novelsystems, methods, apparatus and software of such character.

2. Description of the Related Art

The field of error control coding was revolutionized in 1993 with theinvention of turbo codes. With the use of turbo codes, it is possible toachieve extremely low error probabilities at low signal to noise ratioswith decoding circuitry that is within the realm of practicalimplementation. A turbo code system can be thought of as a way offorming a very strong code from a suitable combination of two or moreweak codes. The goal is to achieve the performance of the strong codewith the decoding complexity implied by the weak codes. One importantfactor in the success of a turbo code design is that most of the errorsequences that cause one of the constituent codes to fail must bedecoded correctly by the other constituent code (this property beingimplied by the constraint that the overall code must be stronger thaneach individual code). The most basic turbo code system operated by (1)encoding a stream of data using one recursive convolutional code, (2)permuting (“interleaving”) the same stream of data, (3) encoding thepermuted data using a recursive convolutional encoder, and (4)transmitting both streams as the signal.

At the receiving end of the basic turbo code system, decoding proceedediteratively. In particular, a first decoder decoded the receiveddemodulated sequence for the first convolutionally coded stream. Then,the resulting estimates (and associated estimates of the reliability ofthose estimates) were interleaved and fed to a second decoder, whichused them as an aid in decoding the second convolutionally encodedsequence. The resulting estimates for the second decoder were thende-interleaved and fed to the first decoder for the first sequence.Finally, they were used in a second pass of decoding. This procedure mayhave continued for several iterations as desired.

One important feature of turbo code communications systems is an elementreferred to as an “interleaver” (or, alternatively, “permuter” or“shuffler”). The general function of an interleaver is to receive a setof bits or symbols and to rearrange them into a different order.

In designing a useful interleaver there are two competing goals: theinterleaver should have high performance and it should have lowimplementation complexity. Several different design rules have beensuggested for the design of turbo code interleavers and two interleaverattributes are widely accepted as reliable indicia of interleaverperformance. The first is “separation” which requires that two symbolsthat are close together in the original sequence should be far apart inthe interleaved sequence. To a first order approximation, the influenceof one symbol on another declines as the distance between them in thesequence increases. It is, therefore, desirable to preclude thepossibility that two erroneous symbols are in close proximity in boththe original and interleaved sequences. The second is “dispersion.” Alarge dispersion is desirable because the error probability in a turbocode system is driven by a combination of several different types ofbasic failure mechanisms. The use of interleavers with a largedispersion reduces the number of dominant error mechanisms.

These two attributes may be quantified as follows. The “separation” or“s-parameter” of an interleaver is the smallest number such that twoinputs to the interleaver at a distance less than s from each other areguaranteed to be mapped, by the interleaver, to outputs that are atdistance at least s apart. Interleavers may be represented by aninterleave scatter plot, which is a two-dimensional plot in which apoint is plotted for every pair (i, π(i)). Equivalently, the sameinformation may be expressed as an n×n matrix containing a 1 at everypoint of the interleaver scatter plot and 0 elsewhere; this matrix willbe referred to as the permutation matrix associated with theinterleaver. If the interleaver has an s-parameter value of s0, then abox centered at an interleaver point and extending a distance s0 in eachdirection will include no other interleaver points.

Dispersion may be expressed in terms of displacement vectors (Δx=j−i,Δy=π(j)−π(i)) for any pair of inputs i,j where i<j. Dispersion is thenumber of distinct displacement vectors that occur out of the n(n−l)/2possible vectors. The “normalized dispersion” is the ratio of the actualdispersion to the maximum possible dispersion.

The simplest known interleavers are “rectangular” or “block”interleavers. These interleavers store data streams into a rectangulararray row by row, and read out the stored data column by column. Amongpreviously known interleavers, a subclass of the block interleavers areeasily shown to be self-inverting. An N×M block interleaver on blocks ofsize n=N M has permutation function given by π(i)=(M. i) mod (N M−1) ifwe number the positions from 0 to n−1 rather than from 1 to n. Theself-inverting constraint requires that π(π(i))=i. This condition issatisfied if N=M, as then π(π(i))=π(M. i) mod (N M−1)=(M^2 i) mod(M^2−1)=i.

It can be shown that the normalized dispersion of block interleaversapproaches zero. Such an interleaver, however, has an s-parameter of√{square root over (n)} which is the highest possible s-parameter for aninterleaver. Nonetheless, the dispersion of this interleaver is so lowthat it gives poor performance in practice. Furthermore, it is knownthat block interleavers give markedly inferior performance in turbocoding applications because such interleavers are subject to asignificant “error floor” problem, in which error probability decaysvery slowly with increasing signal to noise ratio beyond a given point.This too is a major reason for the poor performance of such blockinterleavers.

Interleavers are used in various places in communications systems.Interleavers with good properties for some applications do notnecessarily work well in the turbo coding framework. Various propertieshave been used to express the quality of an interleaver. For example,separation is a widely used measure of interleaver quality. The blockinterleavers discussed above can provide a very good separation measure.However, for turbo codes, interleavers are needed which simultaneouslyhave several good qualities. For example, it is desirable forinterleavers for turbo coding have good separation and at least oneother good property, such as dispersion. None of the related prior artinterleavers simultaneously offer he qualities of high separation, largedispersion and self-inversion.

As a result of such deficiencies, recent interleaver design efforts havefocused on identifying interleavers that perform better than the basicblock interleavers described above. For example, much work has been doneon pseudo-random or deterministic interleavers, i.e., on the productionof deterministic rules that succinctly describe an interleaver thatperforms well. These include Berrou-Glavieux interleavers, Welch-Costasinterleavers, JPL interleavers, Takeshita-Costello interleavers, andothers. The advantages offered by deterministic interleavers are basedon the recognition that deterministic interleavers consume fewer systemresources compared to unstructured or random interleavers. Thisadvantage, however, is only beneficial if the deterministicspecification can be efficiently implemented in the decoder. For manyapplications, such as a turbo coding chip, the processing of algorithmicinstructions with interleaver circuitry is either not feasible or itselfconsumes excessive resources.

One significant deficiency associated with most conventionalinterleavers is that they result in considerable circuit complexity whenphysically implemented in a communications system. Naturally, thiscomplexity also increases the cost of implementing an effectiveinterleaver. In part, this difficulty arises from the fact thatconventional interleaver design often starts with the derivation of anelegant mathematical formula, and then seeks a circuit design toimplement that formula. Too often, this approach results in acomplicated, inefficient and expensive circuit despite the fact that itmay perform in accordance with a relatively simple and elegantmathematical formula.

This problem is further exacerbated by the fact that, for eachinterleaver designed and implemented, a compatible de-interleaver mustalso be designed and implemented to reverse the interleaving processduring use of a given system. Thus, the negative impact of relying onunnecessarily complex circuitry is typically two-fold.

There is, accordingly, a need in the art for novel and morecost-effective methods, systems and apparatus for reducing errors inturbo code communications systems. Such methods and apparatus shouldyield simpler, or at least less expensive, implementinginterleaver/de-interleaver circuitry while still yielding a level ofeffectiveness that is equal to or greater than conventional turbo codeinterleaving methods and apparatus.

The self-inverting turbo code interleavers of the present inventionprovide the foregoing advantages. Numerous other advantages and featuresof the present invention will become apparent to those of ordinary skillin the art from the following description of the example embodiments,from the claims and from the accompanying drawings.

SUMMARY OF THE INVENTION

The present invention satisfies the above-stated needs and overcomes theabove-stated and other deficiencies of the related art by providingmethods, systems and apparatus for reducing the impact of errors indigital communications systems through the use of self-invertinginterleavers/de-interleavers. In particular, the present invention isdirected to self-inverting interleaving in which both high separationand high dispersion are achieved. The present invention offers thepossibility of nearly halving the amount of necessary circuitry toperform interleaving and de-interleaving functions in a turbo codesystem. For example, significant advantages are achieved in that onephysical implementation of dual-function circuitry can be utilized toperform both interleaving and de-interleaving functions. This eliminatesthe need of the prior art to provide separate circuitry to perform eachof these functions independently and, thereby, reduces the amount ofnecessary circuitry by nearly fifty percent.

The present invention stems from the realization that there is oftenlittle correspondence between the simplicity/complexity of amathematical function and the actual complexity of the circuitrynecessary to implement that function. Ideally,interleaver/de-interleaver designs in accordance with the presentinvention should have high separation and dispersion, and, in addition,should be easy to implement. Thus, the present invention lends designprimacy to the goal of reducing circuit complexity rather than strivingfor concise mathematical expressions. For example, the present inventionenables a large gate savings (by a factor of 2 or more) in theinterleaver implementation.

The present invention provides methods of generating a self-invertingturbo code interleaver from an existing non-self-inverting turbo codeinterleaver specification. In an example implementation of theinvention, a plurality of original cycles of the non-self-invertingturbo code interleaver specification are identified. The original cyclesspecify a mapping of an input bit position to a respective output bitposition for raw data bits to be coded. The last bit identified in eachcycle is mapped to an output position corresponding to the first bit insaid original cycle. Each original cycle containing more than two bitsis broken into new cycles, such that each new cycle contains one pair ofbits. The pair of bits for each successive cycle being taken fromsuccessive pairs of bits of the original cycle beginning with the firstbit in each cycle. Each original cycle which has an odd number of bitsprovides: (i) at least one new cycle containing a pair of bits; and (ii)one new cycle having a single bit. The new cycles define the mappingbetween the input and output bit positions for said self-inverting turbocode interleaver.

The self-inverting turbo code interleaver may have a normalizeddispersion of at least 0.33 and/or a normalized s-parameter of at least33. The original non-self-inverting interleaver may be a blockinterleaver. The block length of the original interleaver may be atleast 1024.

The present invention further provides methods for randomly generating aself-inverting turbo code interleaver. An example implementation of sucha method is as follows:

-   -   (a) setting a minimum target separation value S, such that two        input bits less than S apart at the input are at least S apart        at the output of the interleaver;    -   (b) mapping a first input bit position to a randomly chosen        output bit position j;    -   (c) constraining input position j to map to the first input bit        position, j being randomly chosen from all allowed output        positions which do not violate the target separation value S;    -   (d) for each of the remaining input bits, in sequence:        -   computing all remaining allowed output bit positions of each            successive input bit that does not violate the target            separation value S when an input bit position corresponding            to the allowed output bit position is constrained to map to            an output position corresponding to the respective            successive input bit position;        -   choosing one of the remaining allowed output bit positions            of the respective input bit at random;        -   constraining the input bit position corresponding to the            chosen output bit to map to an output bit position            corresponding to the respective successive input bit            position.

In the event that step (d) results in failure when no remaining outputbit positions are allowed for one of the remaining input bits,discarding results of steps (b–d) and repeating steps (b–d) until all ofthe input bits are mapped to corresponding allowed output values.

Alternatively, in the event that step (d) results in failure when noremaining output bit positions are allowed for one of the remaininginput bits, discarding results of step (d) and repeating step (d) untilall of said remaining input bits are mapped to corresponding allowedoutput values.

In a further example implementation, in the event that step (d) resultsin failure when no remaining output bit positions are allowed for one ofthe remaining input bits, discarding results of step (d) for a selectednumber of m previous bits in the sequence prior to said failure andrepeating step (d) beginning with said mth previous bit in saidsequence. The number m of previous bits may vary with each successiveiteration of step (d).

The present invention is further directed to methods and apparatus forencoding a data stream using self-inverting turbo code interleavers.Further, methods and apparatus are provided for communicating a datastream, which utilize self-inverting turbo codeinterleavers/de-interleavers to perform error-correction on the datastream sent via the communications system. The self-inverting turbo codeinterleaver/de-interleaver of the present invention has at least one ofa normalized s-parameter of at least 33 and/or a normalized dispersionof at least 0.5. The “normalized” dispersion is the ratio of the actualdispersion to the maximum possible dispersion. The “normalized”s-parameter is the ratio of the actual s-parameter to the maximumpossible s-parameter, and may be expressed as 100(s/√{square root over(n)}).

In an example embodiment of the invention, methods and apparatus areprovided for encoding and communicating digital data for transmission.In this example embodiment, a parallel encoding scheme is used. Anoriginal data stream is encoded at a first encoder with a firstconvolutional code to produce a first convolutionally coded data stream.A copy of the original data stream is interleaved at a self-invertingturbo code interleaver to produce an interleaved data stream. Theself-inverting turbo code interleaver has at least one of a normalizeds-parameter of at least 33 and a normalized dispersion of at least 0.5.The interleaved data stream is encoded at a second encoder with a secondconvolutional code to produce a second convolutionally coded datastream. The first convolutionally coded data stream and the secondconvolutionally coded data stream are then combined to provide acombined data stream. The combined data stream is then modulated at amodulator for transmission via a communications network.

The communications system may comprise at least one of a globalcommunication system, an Internet, an extranet, a wide area network, alocal area network, a wireless network, a combination of interconnectednetworks of various types, or the like.

In an alternate embodiment of the invention, the normalized dispersionmay be at least 0.67 and the normalized s-parameter may be at least 50.

At the receiver side of the communications system, the modulatedcombined data stream is received at a receiver. The modulated combineddata stream is demodulated at a demodulator. The first convolutionallycoded data stream is decoded at a first decoder to produce firstreliability estimates for raw data bits of the original data stream. Thefirst reliability estimates are de-interleaved at a first de-interleaverto produce de-interleaved first reliability estimates. The secondconvolutionally coded data stream is decoded at a second decoder usingthe de-interleaved first reliability estimates to produce secondreliability estimates for the raw data bits of the original data stream.The second reliability estimates are then de-interleaved at a secondde-interleaver to provide de-interleaved second reliability estimates. Afeedback loop is provided for feeding the de-interleaved secondreliability estimates into the first decoder for second pass decodingand de-interleaving of the first and second convolutionally coded datastreams to recover the original data stream.

Those skilled in the art will appreciate that additional decoding andde-interleaving passes may be performed, as necessary, to recover theoriginal data stream.

In a further example embodiment in accordance with the presentinvention, the encoding of the digital data stream may occur in a serialmanner. In this example embodiment, the original data stream is encodedat a first encoder with a first convolutional code to produce a firstconvolutionally coded data stream. This first convolutionally coded datastream (rather than the original data stream as in the exampleembodiment described above) is then interleaved using a self-invertingturbo code interleaver having at least one of a normalized s-parameterof at least 33 and a normalized dispersion of at least 0.5 to produce aninterleaved data stream. The interleaved data stream is then encoded ata second encoder with a second convolutional code to produce a secondconvolutionally coded data stream. The first convolutionally coded datastream and the second convolutionally acoded data stream are thencombined to provide a combined data stream. This combined data stream isthen modulated for transmission via a communications network. Therecovery of the original data stream at the receiver side occurs in thesame manner as described in connection with the parallel encoding schemedescribed above.

The interleavers provided by the present invention may be implemented inthe form of a semiconductor chip for performing turbo codeerror-correction wherein the chip includes an interleaver/de-interleaverfor interleaving a data stream prior to transmission via thecommunications system, wherein the interleaver/de-interleaver having anormalized s-parameter of at least 33 and a normalized dispersion of atleast 0.5, and wherein the interleaver/de-interleaver alsode-interleaves the received data stream to thereby recover the datastream from the received data stream. The semiconductor chip may be aprocessor chip with a demodulator, a detector, a decoder, and the like.The chip may also be a cellular telephone integrated circuit.

For illustration purposes, a simplified example of a turbo coding methodis provided. Assume that raw data bits 10011 are input into an encoderblock. The encoder block, using a turbo code, takes the five raw databits 10011 and outputs, for example, 15 data bits. The turbo code mayuse two smaller constituent codes, code 1 and code 2. The raw data bitsare sent through code 1, providing 5 “new” parity bits of output. Forexample, for code 1, input of raw data bits 10011 may provide 1001101110 output. For code 2, the raw data bits are fed in, but they arescrambled first (i.e., interleaved). This portion of the encoder blockis the “turbo code interleaver”. As an example, the scrambling rule mayrequire that bit 1 moves to bit 4, bit 4 moves to bit 2, bit 2 moves tobit 1, and bits 3 and 5 interchange. This scrambling rule may be writtenas (1->4->2) (3->5), where the last bit in each cycle is understood tomap back to the first (2->1 and 5->3). This may sometimes be writtenwithout the arrows as (1 4 2) (3 5). Therefore, the raw data bits 10011would be scrambled to provide 01110, which is fed into code 2. As anexample, code 2 may output 01110 11000 (i.e., that the parity bits ofcode 2 are 11000 based on the scrambled input). The overall output ofthis (relatively small) turbo coding system would be 10011 01110 11000.The scrambled raw data (i.e., 01110) is usually not sent in addition tothe true raw data (i.e., 10011). Once this data has been output by theturbo coder, there are many other operations that are performed on thedata as will be apparent to those skilled in the art which are notpertinent to the present invention (e.g., modulating the data with acarrier signal, and the like). The foregoing turbo coding example is asimplistic example and does not describe a self-inverting interleaver.An interleaver is self-inverting if and only if it interleaves the rawdata by interchanging bit positions with one another or leaving bits inthe original position. The above example is not self-inverting, as itsends bit 1 to bit 4, but does not send bit 4 to bit 1.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will hereinafter be described in conjunction withthe appended drawing figures, wherein like numerals denote likeelements, and:

FIG. 1 shows a block diagram of an example embodiment of the presentinvention;

FIG. 2 shows a block diagram of a further example embodiment of thepresent invention; and

FIG. 3 shows an example scatter plot for an 11×11 self-invertinginterleaver.

DETAILED DESCRIPTION

The ensuing detailed description provides exemplary embodiments only,and is not intended to limit the scope, applicability, or configurationof the invention. Rather, the ensuing detailed description of theexemplary embodiments will provide those skilled in the art with anenabling description for implementing an embodiment of the invention. Itshould be understood that various changes may be made in the functionand arrangement of elements without departing from the spirit and scopeof the invention as set forth in the appended claims.

FIG. 1 shows an example embodiment of a communication system 10 inaccordance with the invention which utilizes a parallel encoding scheme.Data stream 5 is split to provide parallel inputs into the system 10.The data stream 5 is encoded at encoder 12 with a first recursiveconvolutional code to create a first convolutionally coded data stream.Simultaneously, the data stream 5 is interleaved atinterleaver/de-interleaver 14 using a self-inverting interleaver inaccordance with the present invention. Then, the interleaved data streamis output from the interleaver 14 and is encoded at a second encoder 18with a second recursive convolutional code to create a secondconvolutionally coded data stream. The first convolutionally coded datastream from the first encoder 12 and the second convolutionally codeddata stream from the second encoder 18 are then combined at combiner 17and then modulated for transmission at modulator 15.

The modulator 15 encompasses all operations required to turn the encodedbit stream into a signal suitable for transmission over a communicationchannel. These operations may include, but are not limited to,scrambling, symbol interleaving, mapping to signal space symbols, pilotinsertion, cyclic prefix addition, and the like. These are elements thatare not essential to the current invention and are also familiar tothose skilled in the art.

The signal output from the modulator is provided to a transmitter 16 fortransmission to a receiver 20. The signal is received at the receiver20. The received signal is demodulated at demodulator 21 to provide thecombined data stream including the first and second convolutionallyencoded data streams. Those skilled in the art will appreciate that thedemodulator 21 provides functions analogous to those of the modulator15. A first decoder 22 decodes the first convolutionally coded stream,producing first reliability estimates for each of the underlying rawdata bits of the original data stream. These first reliability estimatesfrom the decoding of the first convolutionally encoded data stream arescrambled at interleaver/de-interleaved 24 using a self-invertinginterleaver in accordance with the present invention. These scrambled(i.e. de-interleaved) estimates are input into a second decoder 26 foruse in decoding the second convolutionally coded data stream. Decoder 26produces second reliability estimates for each of the underlying rawdata bits of the original data stream. Finally, de-interleaving of thesesecond reliability estimates occurs at interleaver/de-interleaver 28.The results from de-interleaver 28 are fed back to the first decoder 22,and are used in a second pass of decoding. This procedure may berepeated for several iterations, as desired, to recover the originaldata stream 5′ at the output of the communication system 10.

An example embodiment of a communication system in accordance with theinvention which utilizes a serial encoding scheme is shown in FIG. 2.Data stream 5 is encoded at encoder 12 with a first recursiveconvolutional code to create a first convolutionally coded data stream.The first convolutionally coded data stream is then interleaved atinterleaver/de-interleaver 14 using a self-inverting interleaver inaccordance with the present invention. Then, the interleaved data streamis output from the interleaver 14 and is encoded at a second encoder 18with a second recursive convolutional code to create a secondconvolutionally coded data stream. The first convolutionally coded datastream, in addition to being provided to interleaver 14, is also outputfrom the first encoder 12 and combined with the second convolutionallycoded data stream from the second encoder 18 at combiner 17. Thecombined data stream from combiner 17 is then modulated for transmissionat modulator 15 as discussed above to provide a signal for transmissionfrom transmitter 16. The functions of the receiver 20, demodulator 21,first decoder 22, interleaver/de-interleaver 24, second decoder 26, andinterleaver/de-inerleaver 28 remain as described in connection with theexample embodiment shown in FIG. 1

As noted above, one aspect of the present invention is the use of“self-inverting” interleavers/de-interleavers. The quality ofself-inversion is defined as follows: given any permutation, there is aleast number i such that the permutation applied i times leaves the datain the original order where i is the period of permutation. For example,the small turbo coding interleaver provided as an example above wasdefined by (1->4->2) (3->5), which has a period of six. A self-invertinginterleaver applied to interleaved data gives back the original input.Therefore, self-inverting interleavers have a period two permutation(i.e. wherein a second application of the permutation restores allelements to their original places).

Self-inverting interleavers can also be expressed in terms of aninterleaver scatter plot/permutation matrix. FIG. 3 shows an examplescatter plot diagram 100 for an 11×11 self-inverting interleaver (i.e.an interleaver having a period of 2). The plot 100 of a self-invertinginterleaver is symmetrical about a diagonal line running from the originat the lower left-hand corner toward the top right at an angle of 45degrees. This line is shown by “o” in FIG. 3, which designates all theboxes for which x=y. In the diagram shown in FIG. 3, the boxes on thex-axis are numbered 1 to 11, going from left to right. The boxes on they-axis are labeled 1 to 11 going from bottom to top. An “X” is given tospecify the particular pattern of the example interleaver used. Forexample, the “X” in box 101 (x=1, y=4) indicates that position 1 goingin to the interleaver is mapped to bit 4 at the output. Theself-inverting property then demands that position 4 in maps to position1 out, i.e., that there is an “X” in box 102 (x=4, y=1).

In the example shown in FIG. 3, an “X” is shown in box 103 (x=5, y=5),indicating that position 5 is a fixed point (i.e. the input to theinterleaver is not changed), which is an acceptable characteristic of aself-inverting interleaver. Also note that there is exactly one X ineach row and column, which is a required characteristic of anyinterleaver.

Those skilled in the art should appreciate that the scatter plot 100shown in FIG. 3 is provided solely for purposes of illustrating theself-inverting properties of the interleaver. The interleaver used togenerate the scatter plot of FIG. 3 was generated without regard tooptimizing its dispersion characteristics or its s-parameter (i.e., thes-parameter of the interleaver illustrated in FIG. 3 is s=1).

Those skilled in the art should also appreciate that the presentinvention may be implemented using substantially self-invertinginterleavers having a permutation matrix that is less than 100%symmetrical about the diagonal (e.g., interleavers having between 90%and 99.999% symmetry about the diagonal). Such interleavers would not betruly self-inverting, as they would require small tweaks to regain theoriginal data. However, such interleavers would still provide many ofthe advantages and benefits of the present invention.

One significant benefit of using a self-inverting interleaver is thatvaluable chip real estate and other resources can be saved by usingidentical interleavers/de-interleavers. By utilizing a self-invertinginterleaver (one in which the interleaver circuitry can also be used asthe de-interleaver circuitry) system resources can be substantiallyreduced relative to conventional designs. Thus, in any application withsignificant circuitry, memory, or other resources connected with theinterleaver, the required resources for each interleaver/de-interleaverare nearly halved.

The set of self-inverting interleavers that have period two isdistinguished in that it forms a very small fraction of all interleaverson blocks of size n, for larger values of n. The total number ofinterleavers on blocks of size n is n!=n (n−1) (n−2) . . . 3 2. Thisnumber rises very quickly (much faster than exponentially) withincreasing n. The number of self-inverting interleavers of size ncontaining no fixed points (that is, no points that are mapped tothemselves by the interleaver) is (n choose n/2) (n/2)!/2^((n/2)), andthe total number of self-inverting interleavers (with fixed pointsallowed) is Σ_(m) (n choose m) (m choose m/2) (m/2)!/2^(m/2). Thisquantity can be shown to be approximately (n/2)! (more precisely, thequantity is (n/2)!^((l+ε)) where ε tends to 0) when n becomes large.Thus the number of self-inverting interleavers on blocks of size n isapproximately the same as the total number of interleavers on blocks ofsize n/2.

On the other hand, although the fraction is small, the actual number ofsuch self-inverting interleavers is large in absolute terms, and, inparticular, is large enough to contain self-inverting interleavers thatperform well when used in turbo coding systems. Consider first anyalgorithm that produces a “good” interleaver for a block of length n/2,that is, the interleaver has a high s-parameter and a high dispersion.If an interleaver of block size n is formed by using two suchinterleavers, with the n/2 inputs from each set mapped to the n/2outputs from the other set, and if these mappings are collected in theappropriate way, we arrive at a symmetric permutation matrix. Itsdispersion is the same as that of the original length n/2 interleaver,so its normalized dispersion is approximately ¼ as large. Thes-parameter constraint is satisfied by any pair of inputs from the sameset. It is possible for this first construction that the s-parameterconstraint could be violated by two inputs that are close to each otherbut on opposite sides of the boundary between the two sets of size n/2.This problem may readily be solved, however, by starting with aninterleaver for a block size of n/2+1 and constraining the last input tobe mapped to itself. This interleaver can again be designed by anymethod applicable to the construction of interleavers. The overallinterleaver of block size n can then be taken by deleting this last rowand forming the same construction as above. This yields a symmetricinterleaver for a block size of n, with the same s-parameter and ¼ ofthe normalized dispersion of the original interleaver. The sameprinciple may be used to design self-inverting interleavers that havehigh performance as measured by separation and dispersion.

It is possible, using various heuristic modifications of standard searchprocedures, to find self-inverting interleavers that have s-parametersand dispersions that are comparable to the best unrestricted (notself-inverting) interleavers. In particular,interleavers/de-interleavers in accordance with the invention have anormalized s-parameter of at least 33 and a normalized dispersion of atleast 0.5. Particularly preferred embodiments of the invention haveinterleavers/de-interleavers with a normalized s-parameter of at least50 and a normalized dispersion of at least 0.67. The performance aboverepresents a lower bound on performance for self-inverting interleaversin accordance with one example embodiment of the present invention. Itshould be noted by those skilled in the art that the achievables-parameters rise in accordance with the length of the block. Themaximum possible s-parameter is provided by √{square root over (n)}achieved by the simple block interleavers mentioned above.Self-inverting interleavers may achieve more than 50% of this maximumvalue, while also providing good dispersion characteristics.

The present invention also includes turbo code interleavers that providereasonable performance and high dispersion. As a starting point, theinterleaver specification for an existing, non-self-invertinginterleaver of a given block length may be used. An example of such aspecification for a non-self-inverting interleaver is provided by the3GPP2 standard code interleaver (as defined in 3^(rd) GenerationPartnership Project 2, document 3GPP2 C.S0002-C, version 1.0, May 28,2002). Such an interleaver may be specified by a complicated algorithmicmethod. The new self-inverting interleaver may be defined from theexisting specification in a way that it is guaranteed to beself-inverting. Such a self-inverting interleaver may be defined byspecifying sets of cycles. For example, the block length 5 interleaverexample provided above (i.e., with raw data bits 10011) is specified bythe rule (1->4->2) (3->5), where the last bit in each cycle isunderstood to map back to the first (2->1 and 5->3). As discussed above,such an interleaver is not self-inverting, since its period ofpermutation is greater than 2. A new interleaver can be defined that isguaranteed to have the self-inverting property by breaking up everyoriginal cycle provided by the non-self-inverting interleaverspecification which contains more than two bits into new cyclescontaining pairs of bits, starting at the beginning of each originalcycle and possibly leaving one bit over in its own new cycle. Continuingwith the example above, this would result in the self-invertinginterleaver being defined by new cycles (1->4) (2) (3->5). Thus bits 1and 4 change positions, bits 3 and 5 change positions, and bit 2 remainsin its original position. Such an interleaver is self-inverting as everynew cycle has a length of 2 at the most. The resulting interleaver willhave high dispersion and will work well within a turbo coding system.However, sometimes such interleavers may not have a high s-parameter.Interleavers created using this method are “deterministic” in the sensethat they are defined by a concise list of steps (i.e., all the stepsrequired to define the original interleaver and the final pairing offstep described above). The interleaver produced by this method is notthe same as the original interleaver, it is merely defined by referenceto it.

An ideal interleaver in accordance with the invention should have a highs-parameter, a high normalized dispersion and should be easy tophysically implement. It has been found that good performance can beobtained by implementing the above-described turbo code communicationssystem with a reasonable amount of complexity. To some extent,complexity is a matter of design choice and is largely a function of themethod of decoding of the two constituent convolutional codes togetherwith the number of decoding iterations. It is well known that the biterror probability at the output of a turbo decoder is approximatelyinversely proportional to the block length of the interleaver.Therefore, lower error probabilities can be achieved by utilizinginterleavers/de-interleavers with longer block sizes.

A randomized method can be used to generate non-self-invertinginterleavers. This method involves setting a target separation value sin advance. The method starts by mapping position 1 to a randomly chosenposition. The next step involves mapping position 2. Due to the targetseparation value, there are constraints on the position this can map to.The method computes all allowed values of the mapped position 2 that donot violate the separation target, and chooses one of these at random.The procedure continues to map further positions in the same way, aslong as this is possible. If at any step there are no possible outputpositions to map the next input position to, the procedure terminates infailure. The method is generally applied by running multiple runs of themethod at a given interleaver length and target separation, until onesuccessful run is obtained. The resulting dispersion tends to be gooddue to the randomized nature of the algorithm; if it is not, theprocedure may be re-run.

An improvement contemplated by the present invention generates goodself-inverting interleavers by constraining the choices at each stepdescribed above by the self-inverting property. In choosing the outputposition, say j, corresponding to input position 1, the input j issimultaneously constrained to map to output 1. Due to this constraint,not all output positions j are allowed for input position 1, as somepositions may violate the separation constraint. This method computesall allowed output positions and chooses randomly among these. Theprocedure then continues analogously as to the remaining input bitpositions with the procedure outlined in the preceding paragraph. Whenthere are further positions to assign but no allowed output values forthem, the procedure set forth in the preceding paragraph gives up infailure. With the present invention, in the event of such a failure theentire process, or only certain portions of the process, may be undoneand rerun until all input bit positions are successfully mapped.

For example, in the event of such a failure, the results can bediscarded and the process can begin again staring with the mapping of afirst input bit position to a randomly chosen output bit position.Alternatively in the event of such a failure, the results of the mappingof the remaining input bit positions may be discarded and process may bererun using the determined mappings for input position j and outputposition j.

As further option in the event of failure, the last m choices can beundone, where m is a heuristically set design parameter, and theprocedure is then continued from that point. The failure terminationcriterion is based on an overall runtime limit. Multiple runs of themethod with various choices for m are then carried out. This methodtends to give successful runs with much higher target separations. Thisis contrasted with the method of the preceding paragraph, which isrelatively unlikely to support high separations in one pass. Such highseparations are expected to be supportable, however, if somebacktracking is allowed as described herein.

Two examples self-inverting turbo code interleavers in accordance withthe present invention are provided in Appendix A attached hereto. Thoseskilled in the art should appreciate that the example self-invertinginterleavers set forth in Appendix A are just two examples ofinterleavers in accordance with the present invention, and otherself-inverting turbo code interleavers with longer or shorter blocklengths may also be generated which have the desired s-parameter anddispersion characteristics.

It should now be appreciated that the present invention providesadvantageous methods and apparatus for generating self-inverting turbocode interleavers, as well as methods and apparatus for encoding andcommunicating a data stream utilizing such self-inverting turbo codeinterleavers.

Although the invention has been described in connection with variousillustrated embodiments, numerous modifications and adaptations may bemade thereto without departing from the spirit and scope of theinvention as set forth in the claims.

1. A method of generating a self-inverting turbo code interleaver froman existing non-self-inverting turbo code interleaver specification,comprising: identifying a plurality of original cycles of thenon-self-inverting turbo code interleaver specification, said originalcycles specifying a mapping of an input bit position to a respectiveoutput bit position for raw data bits to be coded, where the last bitidentified in each cycle is mapped to an output position correspondingto the first bit in said original cycle; breaking up each original cyclecontaining more than two bits into new cycles, each new cycle containingone pair of bits, said pair of bits for each successive cycle beingtaken from successive pairs of bits of said original cycle beginningwith the first bit in each cycle, wherein each original cycle having anodd number of bits provides: (i) at least one new cycle containing apair of bits; and (ii) one new cycle having a single bit; wherein saidnew cycles define the mapping between the input and output bit positionsfor said self-inverting turbo code interleaver.
 2. A method inaccordance with claim 1, wherein the self-inverting turbo codeinterleaver has a normalized dispersion of at least 0.33.
 3. A method inaccordance with claim 2, wherein said self-inverting turbo codeinterleaver has a normalized s-parameter of at least
 33. 4. A method inaccordance with claim 1, wherein said non-self-inverting interleaver isa block interleaver.
 5. A method in accordance with claim 4, whereinsaid block length of said interleaver is at least 1024.